The module of splines on a polyhedral complex can be viewed as the syzygy module of its dual graph with edges weighted by powers of linear forms. When the assignment of linear forms to edges meets certain conditions, we can decompose the graph into disjoint cycles without changing the isomorphism class of the syzygy module. Thus we can use this decomposition to compute the homological dimension...

We give formulae for a module presentation of the module of identities among relations for a presentation of a group, in terms of information on 0and 1-combings of the Cayley graph. This is seen as a special case of extending a partial free crossed resolution of a group given a partial contracting homotopy of its universal cover.

Every simple module having character height at most one for a restricted Cartantype Lie algebra g can be realized as a quotient of a module obtained by starting with a simple module S for the homogeneous component of degree zero in the natural grading of g, extending the action trivially to positive components and inducing up to g. It is shown that if S is not restricted, or if it is restricted...

In this work we introduce a new concept, namely, τ s τs -extending modules (rings) which is torsion-theoretic analogues of extending and then extend many results from to concept. For instance show that for any ring R with unit, if $_{R}R$ purely only every cyclic -nonsingular -module flat. Also, make classification the direct sums rings be -extending.

let $r$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎let $m$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎then $m$ has a direct decomposition $m=oplus_{iin i} m_i$‎,‎where each $m_i$ is noetherian quasi-projective and each‎‎endomorphism ring $end(m_i)$ is local‎.

We are extending to linear recurrent codes, i.e., to time-varying convolutional codes, most of the classic structural properties of fixed convolutional codes. Those results are obtained thanks to a module-theoretic framework which has been developed in linear control.

Deductive verification of object-oriented programs suffers from the lack of modularity. One of the obstacles to modular verification are invariant contracts, which classes extending a verified system could break. We introduce a concept of modules for Java and their correctness w.r.t. invariant contracts and give a theoretical criterion on attributes called module-protection. To ensure modular f...